Most Britons report being satisfied with life, with concerns over work and precarious finances outweighed by happiness gained from children, relationships and where people live, according to a survey by the Office for National Statistics.

The survey of 4,200 adults, conducted between April and August 2011, is part of the prime minister's £2m drive to get a better measure of how the country is doing rather than just focusing on GDP. The ONS's work showed that on average people rated their life satisfaction at 7.4 out of 10. When asked whether things they did in life were worthwhile, people on average gave a score of 7.6.

However, there were signs of stress seeping through British society. Satisfaction with respondents' financial situation had the lowest mean score of 6.2 out of 10, followed by work situation, with 6.7 out of 10. When asked specifically about satisfaction with the balance between time spent on paid work and on other aspects of life, low scores were also given, with an average of 6.4 out of 10.

People were most satisfied with their personal relationships and mental wellbeing, which had the highest mean scores – both scored at 8.3 out of 10. Also of concern to policymakers will be the answer given to the question: "Overall, how anxious did you feel yesterday?" More than a quarter rated this 5 out of 10 – where 10 was feeling "completely anxious".

Lord Layard, the LSE economics professor, said it was likely that life satisfaction would fall as the recession hit. "We know from other European countries that this is sensitive to business cycles and in recessions life satisfaction drops."

The peer, who founded of the Action for Happiness movement to promote well-being, said policymakers could use the data to ameliorate the pain of recession. But they would need to first identify how to measure happiness, then work out what makes people "miserable or happy" and lastly quantify how much happiness one can create by spending taxpayers' cash. "That can be on supporting childcare, parenting or help for mental health".

Layard, a Labour member of the upper house, to argue against expending too much political energy on flattening inequalities. "Although I believe that one pound to a poor person means more than to a rich person and more equal societies are happier, I don't think redistribution of income is by any means the thing that will produce a happier populace."

The science of wellbeing has become fashionable, with the Himalayan Buddhist kingdom of Bhutan cited by Cameron as pioneering the idea of "gross national happiness" and France's President Sarkozy asking the Nobel laureates Joe Stiglitz and Amartya Sen how to measure it.

In fact, happiness has a long academic heritage – beginning in western thought with the Greek philosopher Aristotle. "Aristotle talked about eudaimonia which loosely translates as happiness. But he said there was more to life than how we feel than just pleasure and pain. It was about how we develop our potential and work with our communities," Felicia Huppert at Cambridge University's centre of wellbeing said, pointing out the ONS had posed a "eudaimonic" question in asking about the "things in life that were worthwhile".

Huppert said that "probably the most important work recently was that of Jonathan Haidt (professor of psychology at the University of Virginia) who looked at a moral theory and talked about importance of relationships." Haidt identified five values in societies: care, fairness, loyalty, respect and purity – and suggested US liberals priveleged the first two over the last three.

Huppert, professor of psychology, said: "A lot of young people think that wealth and celebrity will make you happy. In fact the data shows it is about relationships and engagement and feeling that you contribute."

Paul Allen of the ONS said another big factor in happiness was health. "We see that people who responded that when their health was bad that they would report anxiety. What we are trying to build up is a picture of how people rate happiness."

One of the most revealing aspects of the emerging science around happiness is about language. Britons associated happiness with being "calm, relaxed and peaceful" rather than "energised and excited". Allen said this could be seen in the placards held up by strikers on Wednesday's marches. "They held up signs saying: 'We are not happy about this.' It was very British."

On a scale of one to 10, how happy would you say you are?

Pamela Furness, 21, fitness instructor from Hertfordshire: "I'm a seven or eight. I haven't got too much to worry about. I haven't got a mortgage and I'm happy with my job. I'm quite fortunate because the government says there are lots of 16- to 24-year-olds with no job."

Adam Brown, 18, student from Derby: "A few days ago I was an eight, but now I'm a five, probably because I was with my friends and now I have to travel and spend my money on a ticket. I'm a very positive person; I don't get angry at people or anything."

Abi Falodi, 28, engineer from London: "Six. If you've got an income that can pay the bills and you've got friends and family and they're happy, that makes you happy. I've just got a job in Oxford but I've found out that Oxford is not a very cheap place to live. You just have to hope that with time, you get what you want."

Paul Sabini, 49, chef from London: "I'm happy because I think that Tottenham are going to finish above Arsenal."